for the dynamic mobility of spherical particles which is ap-A theory for the dynamic electrophoretic mobility m of spherical plicable for all ka (k is the Debye-Hu ยจckel parameter and colloidal particles in concentrated suspensions in an oscillating a is the particle radius) at zero particle permittivity and electric field is proposed on the basis of Kuwabara's cell model. low zeta potentials. The dynamic mobility has also been The dynamic mobility depends on the frequency v of the applied calculated for other types of particles than a spherical rigid electric field and the particle volume fraction f as well as on particle. Lowenberg and O'Brien (10) derived a dynamic the reduced particle radius ka (where k is the Debye-Hu ยจckel mobility formula of spheroidal particles with thin double parameter and a is the particle radius) and the zeta potential z.
layers. O'Brien (11) calculated the dynamic mobility of a
A mobility formula which involves numerical integration is obporous particle. Ohshima (12) derived a general expression tained for particles with zero permittivity and low z. It is found that the mobility magnitude decreases with decreasing ka as in for the dynamic mobility of cylindrical colloidal particles as the static case ( v ร
0) and as in the single particle case ( f r 0) well as its approximate analytic mobility formula.
and that it decreases with increasing v as in the single particle
The above theories, however, deal with single particles case. However, the f dependence of the mobility magnitude is and thus they can be applied only to very dilute suspensions, much more complicated. Namely, for small ka the mobility magnii.e., suspensions having very small particle volume fractions. tude decreases with increasing f as in the static case. For large A few theoretical studies on concentrated suspensions have ka it increases with increasing f. For moderate ka and not very been made for the limiting case of the static electrophoresis low v the mobility magnitude may exhibit a maximum. In all problem (13-16). The theories of Levine and Neale (13) cases the v dependence of the mobility magnitude becomes less and Kozak and Davis (14-16) for electrokinetics of a swarm as f increases, that is, the dynamic mobility at any v approaches of identical particles take into account particle-particle inthe static mobility as f increases. An accurate mobility formula teractions by means of Kuwabara's cell model ( 17). This without involving numerical integration applicable for all ka at zero particle permittivity and low z is also derived. This formula model assumes that each particle is surrounded by a virtual is applicable even for high z at ka r ฯฑ unless the dynamic relaxcell such that the particle/solution volume ratio in a unit ation effect becomes appreciable. แญง 1997 Academic Press cell is equal to the particle volume fraction throughout the Key Words: dynamic electrophoretic mobility; spherical particle; entire system and the fluid vorticity is zero at the outer oscillating electric field; concentrated suspension. surface of the cell. Kozak and Davis ( 14) extended the theory of Levine and Neale (13) to the case of an array of circular cylinders. Kozak and Davis (15,16) also developed 137